Analytical Calculations Research Articles

Analytical calculation approach for rocket nose cone structure with orthotropic material

The Authors of this research developed an analytical calculation method to estimate the strength of nose cone structures made of orthotropic materials, which were crucial components in aircraft and spacecraft. Strength analysis of nose cones had been comprehensively addressed for isotropic materials; however, the lack of efficient approaches for orthotropic materials presented a challenge. In this research, a new analytical method was proposed, combining membrane stress theory for isotropic materials with classical laminate theory for orthotropic materials. This approach enabled the determination of stresses on the nose cone shell structure in both meridional and circumferential directions in an efficient and straightforward manner. The analysis results indicated that the developed analytical method exhibited stress distribution trends similar to those obtained using the Finite Element Method. Stresses in the +45° and –45° direction, as well as in-plane shear stress and Tsai-Wu failure indices, showed trend similarity between the two methods. Despite specific numerical differences in the calculation results, these consistent trends suggested that the analytical method could serve as a tool for the preliminary design of a nose cone structure with a similar configuration analyzed in this study.

An acceleration-radiation model for nonthermal flares from Sgr A*

is the electromagnetic counterpart of the accreting supermassive black hole in the Galactic center. Its emission is variable in the near-infrared (NIR) and X-ray wavelengths on short timescales (several minutes to a few hours). The NIR light curve displays red-noise variability, while the X-ray light curve exhibits bright flares that rise by many orders of magnitude upon the stable X-ray quiescent emission. Every X-ray flare is associated with a bright NIR flux change, but the opposite is not always true. The physical origin of NIR and X-ray flares is still under debate. We introduce a model for the production of NIR and X-ray flares flares from an active region in where particle acceleration takes place intermittently. A fraction of electrons from their thermal pool is accelerated to higher energies while they radiate via synchrotron and synchrotron self-Compton (SSC) processes. in contrast to other radiation models for flares, the particle acceleration is not assumed to be instantaneous. We studied the evolution of the particle distribution and the emitted electromagnetic radiation from the flaring region by numerically solving the kinetic equations for electrons and photons. Our calculations took the finite duration of particle acceleration, radiative energy losses, and physical escape from the flaring region into account. To gain better insight into the relation of the model parameters, we complemented our numerical study with analytical calculations. Flares are produced when the acceleration episode has a finite duration. The rising part in the light curve of a flare is related to the particle acceleration timescale, while the decay is controlled by the cooling or escape timescale of particles. The emitted synchrotron spectra are power laws whose photon index is determined by the ratio of the acceleration and escape timescales, followed by an exponential cutoff. This occurs at the characteristic synchrotron photon energy emitted by particles with the maximum Lorentz factor (where energy loss and gain rates become equal). The NIR flux increases before the onset of the X-ray flare, and the time lag is linked to the particle acceleration timescale. Bright X-ray flares, such as the one observed in 2014, have gamma -ray counterparts that might be detected by the Cherenkov Telescope Array Observatory. Our generic model for NIR and X-ray flares favors an interpretation of diffusive nonresonant particle acceleration in magnetized turbulence. If direct acceleration by the reconnection electric field in macroscopic current sheets causes the energization of particles during flares in then models considering the injection of preaccelerated particles into a blob where particles cool and/or escape would be appropriate to describe the flare.

Nonperturbative determination of the N=1 supersymmetric Yang-Mills gluino condensate at large N

We present the first nonperturbative large N calculation of the N=1 supersymmetric SU(N) Yang-Mills gluino condensate obtained by means of numerical simulations of the lattice-discretized theory, exploiting large-N twisted volume reduction. We present two different determinations based, respectively, on the Banks-Casher formula and on the Gell-Mann–Oakes–Renner relation, both giving perfectly consistent results. By expressing the lattice results in the Novikov-Shifman-Vainshtein-Zakharov (NSVZ) scheme, we are able for the first time to compare numerical and analytic computations. Our most accurate determination of the renormalization group invariant (RGI) gluino condensate gives ΣRGI/ΛNSVZ3=[1.18(08)stat(12)syst]3=1.64(33)stat(50)syst=1.64(60), in agreement with the N dependence and the value predicted by the weak coupling instanton-based approach ΣRGI/ΛNSVZ3=1. Published by the American Physical Society 2024

High-order schemes of exponential time differencing for stiff systems with nondiagonal linear part

Exponential time differencing methods are a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models often possess fast oscillating or decaying modes—in other words, are stiff systems. Practical implementation of these methods for the systems with nondiagonal linear part of equations is exacerbated by infeasibility of an analytical calculation of the exponential of a nondiagonal linear operator; in this case, the coefficients of the exponential time differencing scheme cannot be calculated analytically. We suggest an approach, where these coefficients are numerically calculated with auxiliary problems. We rewrite the high-order Runge–Kutta type schemes in terms of the solutions to these auxiliary problems and practically examine the accuracy and computational performance of these methods for a heterogeneous Cahn–Hilliard equation, a sixth-order spatial derivative equation governing pattern formation in the presence of an additional conservation law, and a Fokker–Planck equation governing macroscopic dynamics of a network of neurons.

Error performance of DF cooperative SMTs with I/Q imbalance over Beckmann fading channels

The direct down-conversion principle, which has generally been used in the design of multiple-input multiple-output (MIMO) schemes, including space modulation techniques (SMTs), is attractive to researchers because of its low cost, low power consumption with fewer components, flexible and simple structure. However, hardware imperfections such as in-phase (I) and quadrature-phase (Q) imbalance (IQI) negatively affect the performance of the systems with direct down-conversion in practice. On the other hand, cooperative communication is a promising technology that can be utilized in the design of future wireless networks due to its significant advantages such as increasing system reliability, extending network coverage, reducing channel degradation, and providing high quality of service. In this study, SMT-based methods are integrated into cooperative systems, and a flexible and comprehensive model is presented that is applicable to many channel structures. Specifically, the error performance analysis of space shift keying (SSK), spatial modulation (SM), and quadrature SM (QSM) systems in the presence of IQI in decode-and-forward (DF) cooperative communication is carried out by analytical derivations and computer simulations over generalized Beckmann fading channels. The obtained results show that the performance of SMT-based DF cooperative systems is superior to the conventional schemes, and the effects of receiver IQI can be eliminated by optimal detector designs.

Analytical Theory of Reflection of Hydrogen Isotopes of Thermonuclear Energies from Construction Materials

A theoretical description of reflection of hydrogen isotopes from a solid body based on data available in modern literature on the cross sections for elastic and inelastic scattering of ions is presented. The results of the analytical calculation are compared with the results of computer simulation and experimental data. The interaction of hydrogen isotopes with energies from 300 eV to 25 keV with materials in a wide range of atomic numbers, namely Be, C, Ti, Ni, W, Au, is considered. A critical review of existing analytical models of multiple scattering of light ions in solids is performed.

Toward a computational mixed methods framework to measure online deliberative discourse

This article proposes and tests a reproducible framework for a computational method to measure social media-based deliberative discourse by analyzing commentary surrounding the Canadian convoy protests of COVID-19 vaccine mandates and restrictions. Employing a combination of analytic calculations, alongside tools such as Google Perspective and Linguistic Inquiry and Word Count (LIWC), this article assesses the quality of online deliberative discourse using established measures of deliberation including the variables rationality, interactivity, equality, and civility. We propose computational approaches to measuring these variables, and work toward validating our approach by observing correlations between an established computational measure of online deliberation-cognitive complexity. This computational approach is tested using Twitter and Reddit commentary related to the convoy protests that took place in Ottawa, Canada, during February 2022, which influenced the emergence of similar protests around the world. In addition to testing our proposed online deliberative discourse measurement framework, this case study provides insight into the deliberative characteristics of the Twitter and Reddit social media platforms.

Nonequilibrium dynamics and atom-pair coherence in strongly interacting Bose-Fermi mixtures

Theoretical treatments of nonequilibrium dynamics in strongly interacting Bose-Fermi mixtures are complicated by the inherent non-Gaussian nature of the vacuum two-body physics, invalidating the typical Hartree-Fock-Bogoliubov approximation. Here we apply the cumulant expansion to study nonequilibrium Bose-Fermi mixtures, which allows us to explicitly include the missing non-Gaussian quantum correlations, leading to a consistent dynamical theory of a Bose-Fermi mixture near an interspecies Feshbach resonance. We first apply our theory to a study of atom-pair coherence in the gas, which is significantly enhanced by the competing influences of the Fermi sea and Bose-Einstein condensation, in agreement with analytical calculations. Then we study the depletion of a degenerate Bose-Fermi mixture following a quench to the unitary regime, characterizing the resulting depletion of the Bose-Einstein condensate, the deformation of the Fermi surface, and the production of molecules. We find that at early times, the population dynamics scale quadratically with the hold time, and define an associated characteristic timescale set by the parameters of the mixture and the width of the Feshbach resonance. Published by the American Physical Society 2024

A novel green cloud point extraction-based switchable hydrophilicity solvent method for antimony separation and quantification from various bottled beverages by HGAAS

Herein, switchable hydrophilicity solvent (SHS) was used as a synergistic reagent in the cloud point extraction (CPE) protocol to increase the procedure’s efficiency and sensitivity. At room temperature, the CPE-SHS method was created for the fast and accurate extraction of antimony from a variety of drinks. Hydride generation atomic absorption spectroscopy (HGAAS) was used to antimony detection in various samples following the CPE-SHS protocol. The N,N-dimethylamine (DMA), TritonX-100, and p-tert-butyl-tetrakis[(diethylamide)methoxy]tetrathiacalix[4]arene (BTDMTA) were used as a SHS, surfactant, and chelation reagent, respectively. This procedure’s criteria for validation have been identified, including linearity (0.01–700 µg/L), accuracy, precision, limit of detection (LOD = 0.007 µg/L), limit of quantification (LOQ = 0.023 µg/L), enhancement factor (EF = 160), and matrix influence. This approach was validated using certified reference material. The environmentally friendly practices of this method were assessed using recent tools like Complex Modified GAPI (ComplexMoGAPI) software, Analytical GREEnness Calculator (AGREE) software, Blue Applicability Grade Index (BAGI) software, and Sample Preparation Metric of Sustainability (SPMS) program.

Characterisation and simulation of a general ventilation filter based on a double porosity approach

The air filters installed in ventilation systems are designed for collecting dust and particles. These filters usually consist in folded paper or textile, arranged either as a flat slab or in a V-shape frame. Some of them may also contain activated carbon in order to remove molecular compounds. Experimental results show that they can significantly attenuate the upstream sound sources such as fans or other regenerated noise. Though, these acoustic properties are not strictly speaking designed and often result from the tailored filtering capacities. The present work proposes a three-stage methodology to design and optimize the acoustic performance of these filters. The first stage is the characterization of the intrinsic acoustic parameters of the paper or textile. The second stage consists in the validation of these parameters regarding sound attenuation as measured in impedance tube. This includes analytical and finite element computations to correctly account for the mounting conditions of the specimen in the impedance tube. The final stage consists in predicting the sound attenuation measured on the full-size filter, set in shape using the porous composite material theory. The obtained results provide a satisfactory correspondence allowing for an accurate design at an early stage of the project.

Global active noise control using SIMO near-field systems - Simulation and technical implementation

The technical implementation of a single-input multiple-output (SIMO) active near-field noise control (ANC) system designed for global low-frequency noise control is presented. The SIMO control strategy is motivated by noise control simulations based on a direct boundary element method (BEM) ansatz formulated in this paper. The suitability of the chosen BEM formulation and SIMO control strategy is accompanied and confirmed by extensive experiments and comparison to analytical calculations based on isotropic sources. The influence of parameters such as the positioning of the error microphone, the membrane velocity required for optimal global reduction, the effects of phase inaccuracies and the number of actuators on global reduction are investigated. The real-time control of the SIMO system is technically implemented on field programmable gate array (FPGA) hardware using a frequency domain block FxLMS algorithm. The iterative algorithm converges in less than 0.1 s for the examined frequency range from 100 Hz to 1000 Hz. Measurements using various circular SIMO array configurations showed reductions in sound power of up to 85\%, aligning closely with the numerical results.

Analysis of binary mixture of oxytetracycline and bromohexine in their combined veterinary formulation by four simple spectrophotometric methods with greenness assessment

Tetracyclines family is considered as the first-line antibiotic drugs for food animals. Formulating bromhexine (BR) with oxytetracycline (OTC) improved the antibacterial activity of OTC, besides it is considered as a mucolytic agent. Four precise, rapid, and simple spectrophotometric methods were successfully developed for resolution of the overlapped spectra of OTC and BR in their pure form and in their pharmaceutical formulation. The proposed methods are absorption correction (AC), dual wavelength (DW), induced dual wavelength (IDW), and spectrum subtraction (SS) spectrophotometric methods. The developed methods were used for the determination of OTC and BR in the ranges of 2–50 µg/mL and 1–30 µg/mL, respectively for all methods. For (AC) and (SS) methods, OTC and BR were determined at 380 nm and 245.6 nm, respectively after spectral resolution steps. While for (DW) method, the absorbance difference between λ (271.8 –287.6 nm) and λ (245.6 –283.2 nm) were used for the determination of OTC and BR, in order. For IDW, it depended on using the absorbance difference between 271.8 nm and 245.6 nm as well as the equality factor (F) calculated for each drug at the selected wavelengths. In all methods, HCl was used as a solvent and they are validated according to ICH guidelines. Several green metric tools have been developed to evaluate the greenness of the analytical methods like National Environmental Methods Index (NEMI), Modified NEMI, Analytical Eco-scale, Green Analytical Procedure Index (GAPI) and Analytical GREEnness calculator (AGREE), and all ensured the low impact of the suggested approaches on health and environment. The proposed methods are highly selective, robust and precise. Additionally they are time and money effective and can be used in any analytical laboratory.

Исследование многоуровневых моделей управления вагонопотоками в адрес припортовых станций с применением теории дифференциальных уравнений

Purpose: To consider the issue of sustainability of multi-level control systems for car flows to port railway stations in the conditions of intellectualization of transportation management processes. To assess the influence of three-level and two-level control systems for the operational work of port roads on the quality of planning the supply of trains to port stations under various modes of operational operation of railways. Determine the conditions for the stability of the car flow control system by constructing and studying the corresponding hard and soft mathematical models described by autonomous systems of ordinary linear differential equations. Methods: In this study, the methods of the theory of stability of solutions of differential equations, as well as the theory of control and dynamical systems are used. A phase space is used in a visual representation, a qualitative and quantitative analysis of the behavior of phase trajectories in it is performed, corresponding to undisturbed and perturbed solutions of systems of differential equations describing the constructed models of control systems. Results: A comparison of the characteristics of multistage car traffic control systems is given. A study of the stability of multilevel models of car traffic management in the context of the intellectualization of management functions is proposed. In the environment of the analytical computing system, the conditions of asymptotic stability in time of a two-level wagon traffic control system are found and studied. Practical importance: The results obtained by computational experiment make it possible to assess the stability of the functioning of port-side transport and technological systems in the context of changes in the organization of production and the intellectualization of transportation management processes. Computer mathematics systems make it possible to implement the heuristic component of research and obtain theoretically sound and visual solutions to problems of optimizing cargo and wagon traffic control modes.

Effects of nozzle geometry and fiber orientation on the tensile strength of 3D printed continuous fiber reinforced composites

In material extrusion (MEX) based 3D printing, inter-filament voids are intrinsic to printing process. The void orientation, volume and shape are affected by multiple factors including the nozzle shape, stacking sequence and printing direction. In this study, the adverse effects of the inter-filament voids on tensile properties and damage modes were investigated numerically on 3D printed acrylonitrile butadiene styrene-carbon fiber (ABS/CF) continuous fiber-reinforced composites (CFRCs). Uniaxial tensile simulations were performed considering various nozzle geometries (circular, square), fiber orientations (θ=0o,30o,45o,60o,90o) relative to loading direction, and a regular stacking sequence of extrudates. The extrudate cross-section was modeled either using elliptical or superelliptical extrudates deposited from a circular or square nozzle, respectively. Excellent agreement was seen when the simulated results were benchmarked against several published experimental and numerical work. Simulated results showed that changing the nozzle shape from circular to square improved the mechanical properties across all fiber angles by lowering the void content by 7−8% and increasing the ultimate tensile strength (σT) by 11−18%, tensile stiffness (ET) by 6−8%, and the tensile failure strains (ϵT,fail) by 1−11%. For superelliptical extrudates the number of observed damage modes also reduced, and this is due to a 37.2% and 58.2% improvement in the inter-filament and inter-layer bond lengths, respectively. Also, when fiber angle became increasingly off-axis to tensile load direction, the strengths, moduli, and failure strains reduced for both circular and square nozzles. The significance of using microstructure geometries and explicitly modeling inter-filament voids for simulating MEX printed CFRCs was highlighted by comparing these results with both analytical calculations and simulated results of homogeneous solid CFRC blocks without voids.

Design of a Thermally Resistant and Safe Door for a Medical Waste Pyrolysis Incinerator in a Green Environment

Abstract The door of a medical waste pyrolysis incinerator plays a critical role in ensuring safe and efficient operation, as it must withstand extreme conditions, including combustion temperatures ranging from 1000 °C to 1200 °C and internal pressure. This study focuses on designing a door that is not only robust and airtight but also highly resistant to these high temperatures, ensuring both operational safety and environmental protection. The design process began with a combustion chamber capacity of 0.5 m3, with the incinerator body measuring 900 mm x 900 mm x 1200 mm and the door measuring 650 mm x 650 mm. The door was fabricated using steel with a yield strength of 245 MPa, equipped with locking bolts, and sealed with high-temperature-resistant asbestos to prevent leaks. The design was initially developed using 2D AutoCAD and 3D SolidWorks software. Analytical calculations were validated through SolidWorks simulations, revealing that the stress at the critical point was 58.185 MPa, providing a safety factor of 4.2 times above the yield stress. This robust design not only enhances the durability of the incinerator door but also contributes to the overall safety and effectiveness of medical waste management, supporting broader environmental safety goals.

Shubnikov–de Haas effect in the Falicov–Kimball model: strong correlation meets quantum oscillation

Abstract We present a comprehensive investigation of quantum oscillations (QOs) in the strongly-correlated Falicov-Kimball model (FKM). The FKM is a particularly suitable platform for probing the non-Fermi liquid state devoid of quasiparticles, affording exact Monte Carlo simulation across all parameter spaces.
In the high-correlation regime, we report the presence of prominent QOs in magnetoresistance and electron density at low temperatures within the phase separation state. The frequency behavior of these oscillations uncovers a transition in the Fermi surface as electron density diminishes, switching from hole-like to electron-like. Both types of Fermi surfaces are found to conform to the Onsager relation, establishing a connection between QOs frequency and Fermi surface area.
Upon exploring the temperature dependence of QOs amplitude, we discern a strong alignment with the Lifshitz-Kosevich (LK) theory, provided the effective mass is suitably renormalized. Notwithstanding, the substantial enhancement of the overall effective mass results in a notable suppression of the QOs amplitude within the examined temperature scope, a finding inconsistent with Fermi liquid predictions. For the most part, the effective mass diminishes as the temperature increases, but an unusual increase is observed at the proximity of the second-order phase transition instigated by thermal effects.
As the transition ensues, the regular QOs disappear, replaced by irregular ones in the non-Fermi liquid state under a high magnetic field.
We also uncover significant QOs in the insulating charge density wave state under weak interactions ($0 < U < 1$), a phenomenon we elucidate through analytical calculations.
Our findings shed light on the critical role of quasiparticles in the manifestation of QOs, enabling further understanding of their function in this context.

Taste characterization and molecular docking study of novel umami flavor peptides in Yanjin black bone Chicken meat

Five polypeptides with a potential umami taste were isolated and purified from Yanjin black bone chicken. However, the flavor characteristics and umami mechanism have not been clarified. The umami properties of these five peptides were investigated in this work using a range of analytical techniques, computer simulation, and sensory evaluation. HE-10 and TP-7 exhibited the strongest umami flavors. Furthermore, dose-response experiments showed that the umami peptides enhanced umami by generating peptide mineral chelates. Environmental scanning electron microscopy (ESEM) microstructural analyses supported this finding. The molecular docking results indicated that the five polypeptides bind to four critical amino acid residues, namely Glu217, Glu148, Asp216, and His145, of the T1R1/T1R3 receptor. The binding occurred through van der Waals, electrostatic interactions, hydrogen bonding, and hydrophobic interactions. The main surface forces implicated include aromatic interactions, hydrogen bonding, hydrophilicity, and solvent accessibility.

“Nutation” of electron spins in biradicals

In this work, the nutation of the spins of unpaired electrons in the nitroxide biradical of bis‑methano[60]fullerene was experimentally studied. Nutation frequencies were found in a wide range of microwave field power. To interpret the obtained results, numerical calculations of the nutation of biradicals were carried out for a set of parameters of the spin–spin interaction of a pair of unpaired electrons and for different values of the Rabi frequency of the microwave field. At comparing numerical results with experimental data, we also used the results of analytical calculations of nutation for some model situations. As a result of the analysis of experimental data on nutation, an estimate of the exchange and dipole–dipole interactions for the studied biradical was obtained. They are consistent with the results obtained from analysis of the shape of the EPR spectrum for a given biradical.

Analytical calculation of the kinetic q factor and resonant response of toroidally confined plasmas

Symmetry-breaking perturbations in axisymmetric toroidal plasma configurations have a drastic impact on particle, energy, and momentum transport in fusion devices, thereby affecting their confinement properties. The perturbative modes strongly affect particles with specific kinetic characteristics through resonant mode–particle interactions. In this work, we present an analytical calculation of the kinetic q factor, enabling the identification of particles with kinetic properties that meet the resonant conditions. This allows us to predict the locations and structures of the corresponding resonant island chains, as well as the existence of transport barriers in the particle phase space. The analytical results, derived for the case of a large aspect ratio configuration, are systematically compared to numerical simulations, and their domain of validity is thoroughly investigated and explained. Our findings demonstrate that calculating the kinetic q factor and its dependence on both particle and magnetic field characteristics provides a valuable tool for understanding and predicting the resonant plasma response to non-axisymmetric perturbations. Moreover, this approach can be semi-analytically applied to generic realistic experimental equilibria, offering a low-computational-cost method for scenario investigations under various multi-scale perturbative modes.

Measurements of Lund subjet multiplicities in 13 TeV proton-proton collisions with the ATLAS detector

This Letter presents a differential cross-section measurement of Lund subjet multiplicities, suitable for testing current and future parton shower Monte Carlo algorithms. This measurement is made in dijet events in 140 fb−1 of s=13 TeV proton–proton collision data collected with the ATLAS detector at CERN's Large Hadron Collider. The data are unfolded to account for acceptance and detector-related effects, and are then compared with several Monte Carlo models and to recent resummed analytical calculations. The experimental precision achieved in the measurement allows tests of higher-order effects in QCD predictions. Most predictions fail to accurately describe the measured data, particularly at large values of jet transverse momentum accessible at the Large Hadron Collider, indicating the measurement's utility as an input to future parton shower developments and other studies probing fundamental properties of QCD and the production of hadronic final states up to the TeV-scale.